bio | website | |
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location | University of Copenhagen | |
age | 29 | |
visits | member for | 5 years, 1 month |
seen | 1 hour ago | |
stats | profile views | 8,320 |
Nov 23 |
comment |
cohomology of a variation of wreath product
Consider the maps $(z_1,\ldots,z_n,z_{\sigma(1)}, \ldots,z_{\sigma(n)}) \mapsto (tz_1,\ldots,tz_n,tz_{\sigma(1)}, \ldots,tz_{\sigma(n)})$ for $t \in [0,1]$: this is a homotopy between the identity map and the constant map $(0,0,\ldots,0)$. |
Nov 22 |
comment |
cohomology of a variation of wreath product
Are you sure you're asking the question you intended to ask? The space you wrote down is obviously contractible. You could insist that all $z_i$ are distinct but in this case you would obtain $n!$ copies of the usual configuration space of $n$ ordered points in $\mathbf C$. |
Nov 22 |
reviewed | Close Diffusion Equation |
Nov 22 |
reviewed | Close How to calculate a sequence in Maple |
Nov 18 |
awarded | Nice Answer |
Nov 16 |
awarded | Good Answer |
Nov 13 |
awarded | Enlightened |
Nov 13 |
awarded | Nice Answer |
Nov 12 |
comment |
Framed version of braided monoidal category
You're right, they form a nonsymmetric operad. By the way, I think there are some things you might find useful in Nathalie Wahl's Ph.D. thesis. |
Nov 12 |
comment |
Gerbes and Stacks
I don't really understand you so at least one of us is confused. The fiber over a point of $U_i$ is a groupoid with one object and morphism set $BGL(1)$. |
Nov 12 |
answered | Framed version of braided monoidal category |
Nov 12 |
answered | Gerbes and Stacks |
Nov 11 |
comment |
List of Classifying Spaces and Covers
...and even if you find the previous example too silly, allowing yourself to work with stacks does give you several natural examples, like $\mathrm{SL}(2,\mathbf Z)$ acting on the upper half plane. |
Nov 11 |
comment |
List of Classifying Spaces and Covers
Here's a really dumb non-answer (dumb enough that I only make it a comment), but sometimes I find it useful to think along these lines. Namely, if you permit yourself to think about topological stacks instead of topological spaces, you can take $EG = \ast$ (a single point) and $BG = [\ast/G]$ ($G$ any group). This is the universal and minimal choice of classifying space. |
Nov 11 |
comment |
Synthetic vs. classical differential geometry
There's an interesting recent book by Paugam that you might like (although I've only looked briefly at a few chapters), "Towards the Mathematics of Quantum Field Theory". The goal of his book is to formulate QFT mathematically in the most "correct" way possible, which for him means in terms of SDG, diffeological spaces, and homotopical algebra. |
Nov 10 |
comment |
The properness of a submersion
I don't think this completely answers the question. Consider e.g. $\mathbf R\setminus \{0\} \sqcup \{0\}$ with its natural map to $\mathbf R$, which is a nonproper map with compact connected fibers. To rule out a silly counterexample like this it seems one should use the submersion hypothesis (which your argument doesn't). |
Nov 8 |
awarded | Nice Question |
Nov 8 |
asked | What's the dimension of the space of CM cusp forms? |
Nov 6 |
answered | why are motives more serious than “naive” motives? |
Nov 4 |
accepted | Which mapping class group representations come from algebraic geometry? |